Wormlike surfactant

A significant contribution of rheo-NMR has been to show that the uniform shear-rate assumption may be violated in the case of certain classes of fluids in which pathological flow properties are exhibited. Figure 2.8.10 shows shear-rate maps [26] obtained for the wormlike surfactant system, cetylpyridinium chloride-sodium salicylate in water. While the velocity gradients show no deviation from uniformity at very low shear rates, above a certain critical value yc a dramatic variation in the rate-of-strain across the 7° cone gap is found. In particular a very high shear-rate band is found to exist at the mid-gap. 

This full set of self-consistent equations is clearly very difficult to solve, even numerically. However, good approximations of closed integral type have been proposed. These essentially ignore the s-dependence of the survival and orientation functions, which makes them a physically appeaUng approach in the case of wormlike surfactants [71,72]. For ordinary monodisperse polymers the following approximate integral constitutive equation results ... 

Theoretical studies of the dynamics of self-assemblies of wormlike surfactant micelles have been reported by a number of investigators, such as Cates and coworkers [Turner and Cates, 1991 Marques et al 1994]. Since they are subject to reversible scission and recombination, they are called living polymers. The continuous breaking and repair of the micellar chains provides more complex solution behavior than do reptating polymer chains that is, their stress relaxation mechanisms are a combination of reptation and breaking followed by reassembly. At low frequencies, linear viscoelastic (Maxwell) behavior is predicted and observed for some surfactant systems. However, non-Maxwell behavior was observed in Cole-Cole plots of a number of cationic surfactant systems [Lu, 1997 Lin, 2000]. 

Viscoelastic synergy of wormlike surfactant micelles with hydrophobically modified associating polymers [21-26]... 

Cates ME, Candau SJ (1990) Statics and dynamics of wormlike surfactant micelles. J Phys Cond Matt 2(33) 6869-6892... 

Yesilata B, Clasen C, McKinley GH (2006) Nonlinear shear and extensional flow dynamics of wormlike surfactant solutions. 1 Non-Newt Ruid Mech 133(2-3) 73-90... 

FIG. 1 Self-assembled structures in amphiphilic systems micellar structures (a) and (b) exist in aqueous solution as well as in ternary oil/water/amphiphile mixtures. In the latter case, they are swollen by the oil on the hydrophobic (tail) side. Monolayers (c) separate water from oil domains in ternary systems. Lipids in water tend to form bilayers (d) rather than micelles, since their hydrophobic block (two chains) is so compact and bulky, compared to the head group, that they cannot easily pack into a sphere [4]. At small concentrations, bilayers often close up to form vesicles (e). Some surfactants also form cyhndrical (wormlike) micelles (not shown). 

Instead of the familiar sequence of morphologies, a broad multiphase window centred at relatively high concentrations (ca. 50-70% block copolymer) truncates the ordered lamellar regime. At higher epoxy concentrations wormlike micelles and eventually vesicles at the lowest compositions are observed. Worm-like micelles are found over a broad composition range (Fig. 67). This morphology is rare in block copolymer/homopolymer blends [202] but is commonly encountered in the case of surfactant solutions [203] and mixtures of block copolymers with water and other low molecular weight diluents [204,205]. 

Here, V is the volume of the hydrocarbon chain(s) of the surfactant, the mean cross-sectional (effective) headgroup surface area, and 4 is the length of the hydrocarbon tail in the all-trans configuration. Surfactants with Pcone-shaped and form spherical micelles. For l/3truncated-cone-shaped, resulting in wormlike micelles (the term wormlike is preferred over rodlike to highlight the highly dynamic nature of these micelles). 

This calculation is for spherical micelles, but a similar calculation could be used to obtain estimates of salt concentrations for ionic wormlike micelles. Such salt concentrations for wormlike micelles are expected to be increased in comparison to spherical micelles. In fact, the addition of counterions or a sufficient increase in surfactant concentration often leads to a transition from spherical micelles to wormlike micelles. As the free counterion concentration in solution increases, so does the counterion binding. As a result, electrostatic repulsion between the charged head-groups is increasingly shielded and the mean cross-sectional (effective) headgroup... 

In other cases, several discrete relaxation times or distributions of relaxation times can be found [39]. This is typically the case if the stress relaxation is dominated by reptation processes [42 ]. The stress relaxation model can explain why surfactant solutions with wormlike micelles never show a yield stress Even the smallest applied stress can relax either by reptation or by breakage of micelles. For higher shear rates those solutions typically show shear thinning behaviour and this can be understood by the disentanglement and the orientation of the rod-like micelles in the shear field. 

Living polymers, exemplified by surfactant wormlike micelles, continue to prove fruitful for experimental rheology of transitions between different... 

Some ionic surfactants form long, wormlike micelles in aqueous media, especially in the presence of electrolyte or other additives that decrease the repulsion between the ionic head groups (Raghavan, 2001). These giant, wormlike micelles give rise to unusually strong viscoelasticity because of the entanglement of these structures. 

Trimeric and oligomeric surfactants have also been prepared (Zana, 1995 Sumida, 1998 In, 2000 Onitsuka, 2001). Their CMC values are even smaller than those of the analogous geminis. As the number of hydrophobic groups per molecule increases for gemini quaternary C12 ammonium compounds with polymethylene -(CH2) j spacers, their surface layers become more dense, their micellar microviscosity increases, and their micellar shape changes from spherical to wormlike, to... 

We assume here that the kinetic constants kj,kj,k,k, are independent of the length of micelles and surfactant concentration. Therefore, the relaxation of concentration f)erturbation in solutions of wormlike micelles can be essentially more complicated. Moreover, the relaxation processes enumerated above can influence at a different extent various properties of the non-equilibrium micellar solution. This gives a general possibility to determine all these relaxation times. The first of these relaxation processes can be described by model (5.185). The fifth one corresponds obviously to the fast relaxation process in the Aniansson and Wall model. Recently Waton derived an equation for the relaxation times of fusion and fission in micellar solutions, which can be applied to an arbitrary size distribution of micelles [128]. In the limiting cases of short micelles with a narrow size distribution and wormlike micelles this theory leads to relations (5.192) and (5.194), respectively. 

In aqueous solutions of surfactants at concentrations above the critical micelle concentration (CMC), the molecules self-assemble to form micelles, vesicles, or other colloidal aggregates. These may vary in size and shape depending on solution conditions. In addition to surfactant molecular structure, the effects of concentration, pH, other additives, cosolvents, temperature, and shear affect the nanostructure of the micelles. The presence of TLMs or cylindrical, rodlike, or wormlike micelles at concentrations > CMCii are generally believed to be necessary for surfactant solutions to be drag reducing [Zakin et al., 2007]. 

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